Suppose you ride to school with a friend and often arrive at a certain stop light when it is red. One day she states, €œIt seems like this light is green only 10% of the time when we get here.€ You think it is more oft en than 10% and want to test this. You keep track of the color (green/not green) the next 20 times you go to school and find that 4 times (420 = 20%) the light is green when you arrive. You wish to see if your sample provides strong evidence that the true proportion of times the light is green is greater than 10%. In other words, you are testing the hypotheses
H₀: Ï€ = 0.10 versus H_a: Ï€ > 0.10
where π = the long-run proportion of times the light is green.
Two diff erent approaches were taken in order to yield a p-value and both are shown in the applet output.
€¢ Option 1. A simulation-based test was done and found a p-value of 0.148, showing weak evidence against the null.
€¢ Option 2. A one-proportion z-test was conducted and found a p-value of 0.068, yielding moderate evidence against the null.
a. Which test gives a more valid p-value?
b. Give one or two sentences why you picked the option you did.

Transcribed Image Text:

300 Probability of success (T): 0.1 0.1480 20 Sample size (n): 200 1000 Number of samples: V Animate 100 Draw Samples Total = 1000 O Number of successes Proportion of successes Number of successes Count As extreme as O Summary stats Proportion of samples: 148/1000 = 0.1480 All attempts (last sample) O Two-sided O Exact Binomial E Normal Approximation p-value = 0.0680 (Z = 1.49) Successes (last sample) = 0